Search

The classical solution to the Helmholtz wave equation in spherical coordinates is well known and has found many important applications in wave propagation, scattering, and imaging in optics and acoustics. The separable solution is comprised of spherical Bessel functions in the radial direction and spherical harmonics in the angular directions. The nature of the spherical Bessel functions includes a long asymptotic oscillatory tail at large radii, not conducive to applications where a tight concentration of wave amplitude around a ring is desired, for example in toroidal configurations. However, we have found that certain practical bandpass spectral shapes, centered around a peak frequency, can create a superposition of spherical Bessel functions that effectively concentrate the wave amplitude around a defined ring at the time instant of coherent addition, avoiding the long tail asymptotic oscillations of the single frequency solution. Theoretical solutions are shown for different bandpass spectra applied to the spherical Bessel functions, along with numerical solutions of transient wave propagation using practical hemispherical source shapes. These findings introduce a framework by which ring or toroidal concentrated waves can be produced with a simple bandpass superposition applied to hemispherical source shapes and with reference to the classical solutions in spherical coordinates., Comment: 18 pages; 10 figures

In share wave elastography (SWE), the aim is to measure the velocity of shear waves, however unwanted compression waves and bulk tissue motion pose challenges in evaluating tissue stiffness. Conventional approaches often struggle to discriminate between shear and compression waves, leading to inaccurate shear wave speed (SWS) estimation. In this study, we propose a novel approach known as the difference autocorrelation estimator to accurately estimate reverberant SWS in the presence of compression waves and noise. Methods: The difference autocorrelation estimator, unlike conventional techniques, computes the subtraction of velocity between neighboring particles, effectively minimizing the impact of long wavelength compression waves and other wide-area movements such as those caused by respiration. We evaluated the effectiveness of the integrated difference autocorrelation (IDA) by: (1) using k-Wave simulations of a branching cylinder in a soft background, (2) using ultrasound elastography on a breast phantom, (3) using ultrasound elastography in the human liver-kidney region, and (4) using magnetic resonance elastography (MRE) on a brain phantom. Results: By applying IDA on the unfiltered contaminated wave fields of simulation and elastography experiments, the estimated SWSs are in good agreement with the ground truth values (i.e., less than 2% error for the simulation, 9% error for ultrasound elastography of breast phantom and 19% error for MRE). Conclusion: Our results demonstrate that IDA accurately estimates SWS, revealing the existence of a lesion, even in the presence of strong compression waves. Significance: IDA exhibits consistency in SWS estimation across different modalities and excitation scenarios, highlighting its robustness and potential clinical utility.

Objectives- Several ultrasound measures have shown promise for assessment of steatosis compared to traditional B-scan, however clinicians may be required to integrate information across the parameters. Here, we propose an integrated multiparametric approach, enabling simple clinical assessment of key information from combined ultrasound parameters. Methods- We have measured 13 parameters related to ultrasound and shear wave elastography. These were measured in 30 human subjects under a study of liver fat. The 13 individual measures are assessed for their predictive value using independent magnetic resonance imaging-derived proton density fat fraction (MRI-PDFF) measurements as a reference standard. In addition, a comprehensive and fine-grain analysis is made of all possible combinations of sub-sets of these parameters to determine if any subset can be efficiently combined to predict fat fraction. Results- We found that as few as four key parameters related to ultrasound propagation are sufficient to generate a linear multiparametric parameter with a correlation against MRI-PDFF values of greater than 0.93. This optimal combination was found to have a classification area under the curve (AUC) approaching 1.0 when applying a threshold for separating steatosis grade zero from higher classes. Furthermore, a strategy is developed for applying local estimates of fat content as a color overlay to produce a visual impression of the extent and distribution of fat within the liver. Conclusion- In principle, this approach can be applied to most clinical ultrasound systems to provide the clinician and patient with a rapid and inexpensive estimate of liver fat content.

The utilization of a reverberant shear wave field in shear wave elastography has emerged as a promising technique for achieving robust shear wave speed (SWS) estimation. However, accurately measuring SWS within such a complex wave field remains challenging. This study introduces an advanced autocorrelation estimator based on angular integration known as the angular integral autocorrelation (AIA) approach to address this issue. The AIA approach incorporates all the au-tocorrelation data from various angles during measurements, resulting in enhanced robustness to both noise and imperfect distributions in SWS estimation. The effectiveness of the AIA estimator for SWS estimation is first validated using a k-Wave simulation of a stiff branching tube in a uniform background. Furthermore, the AIA estimator is applied to ultrasound elastography experiments, MRI experiments, and OCT studies across a range of different excitation frequencies on tissues and phantoms, including in vivo scans. The results verify the capacity of the AIA approach to enhance the accuracy of SWS estimation and SNR, even within an imperfect reverberant shear wave field. Compared to simple autocorrelation approaches, the AIA approach can also successfully visualize and define lesions while significantly improving the estimated SWS and SNR in homogeneous background materials, thus providing improved elastic contrast between structures within the scans. These findings demonstrate the robustness and effectiveness of the AIA approach across a wide range of applications, including ultrasound elastography, MRE, and OCE, for accurately identifying the elastic properties of biological tissues in diverse excitation scenarios.

Objective. Limited access to breast cancer diagnosis globally leads to delayed treatment. Ultrasound, an effective yet underutilized method, requires specialized training for sonographers, which hinders its widespread use. Approach. Volume sweep imaging (VSI) is an innovative approach that enables untrained operators to capture high-quality ultrasound images. Combined with deep learning, like convolutional neural networks (CNNs), it can potentially transform breast cancer diagnosis, enhancing accuracy, saving time and costs, and improving patient outcomes. The widely used UNet architecture, known for medical image segmentation, has limitations, such as vanishing gradients and a lack of multi-scale feature extraction and selective region attention. In this study, we present a novel segmentation model known as Wavelet_Attention_UNet (WATUNet). In this model, we incorporate wavelet gates (WGs) and attention gates (AGs) between the encoder and decoder instead of a simple connection to overcome the limitations mentioned, thereby improving model performance. Main results. Two datasets are utilized for the analysis. The public "Breast Ultrasound Images" (BUSI) dataset of 780 images and a VSI dataset of 3818 images. Both datasets contained segmented lesions categorized into three types: no mass, benign mass, and malignant mass. Our segmentation results show superior performance compared to other deep networks. The proposed algorithm attained a Dice coefficient of 0.94 and an F1 score of 0.94 on the VSI dataset and scored 0.93 and 0.94 on the public dataset, respectively., Comment: N/A

In the approaches to elastography, two mathematical operations have been frequently applied to improve the final estimate of shear wave speed and shear modulus of tissues. The vector curl operator can separate out the transverse component of a complicated displacement field, and directional filters can separate distinct orientations of wave propagation. However, there are practical limitations that can prevent the intended improvement in elastography estimates. Some simple configurations of wavefields relevant to elastography are examined against theoretical models within the semi-infinite elastic medium and guided waves in a bounded medium. The Miller-Pursey solutions in simplified form are examined for the semi-infinite medium and the Lamb wave symmetric form is considered for the guided wave structure. In both cases, wave combinations along with practical limits on the imaging plane can prevent the curl and directional filter operations from directly providing an improved measure of shear wave speed and shear modulus. Additional limits on signal-to-noise and the support of filters also restrict the applica-bility of these strategies for improving elastographic measures. Practical implementations of shear wave excitations applied to the body and to bounded structures within the body can involve waves that are not easily resolved by the vector curl operator and directional filters. These limits may be overcome by more advanced strategies or simple improvements in baseline parameters including the size of the region of interest and the number of shear waves propagated within., Comment: 11 pages, 6 figures

The improved diagnostic accuracy of ultrasound breast examinations remains an important goal. In this study, we propose a biophysical feature based machine learning method for breast cancer detection to improve the performance beyond a benchmark deep learning algorithm and to furthermore provide a color overlay visual map of the probability of malignancy within a lesion. This overall framework is termed disease specific imaging. Previously, 150 breast lesions were segmented and classified utilizing a modified fully convolutional network and a modified GoogLeNet, respectively. In this study multiparametric analysis was performed within the contoured lesions. Features were extracted from ultrasound radiofrequency, envelope, and log compressed data based on biophysical and morphological models. The support vector machine with a Gaussian kernel constructed a nonlinear hyperplane, and we calculated the distance between the hyperplane and data point of each feature in multiparametric space. The distance can quantitatively assess a lesion, and suggest the probability of malignancy that is color coded and overlaid onto B mode images. Training and evaluation were performed on in vivo patient data. The overall accuracy for the most common types and sizes of breast lesions in our study exceeded 98.0% for classification and 0.98 for an area under the receiver operating characteristic curve, which is more precise than the performance of radiologists and a deep learning system. Further, the correlation between the probability and BI RADS enables a quantitative guideline to predict breast cancer. Therefore, we anticipate that the proposed framework can help radiologists achieve more accurate and convenient breast cancer classification and detection.

Major topics in medical ultrasound rest on the physics of wave propagation through tissue. These include fundamental treatments of backscatter, speed of sound, attenuation, and speckle formation. Each topic has developed its own rich history, lexicography, and particular treatments. However, there is ample evidence to suggest that power law relations are operating at a fundamental level in all the basic phenomena related to medical ultrasound. This review paper develops, from literature over the past 60 years, the accumulating theoretical basis and experimental evidence that point to power law behaviors underlying the most important tissue-wave interactions in ultrasound and in shear waves which are now employed in elastography. The common framework of power laws can be useful as a coherent overview of topics, and as a means for improved tissue characterization., Comment: 25 pages, 6 figures

Sharing autonomy between robots and human operators could facilitate data collection of robotic task demonstrations to continuously improve learned models. Yet, the means to communicate intent and reason about the future are disparate between humans and robots. We present Assistive Tele-op, a virtual reality (VR) system for collecting robot task demonstrations that displays an autonomous trajectory forecast to communicate the robot's intent. As the robot moves, the user can switch between autonomous and manual control when desired. This allows users to collect task demonstrations with both a high success rate and with greater ease than manual teleoperation systems. Our system is powered by transformers, which can provide a window of potential states and actions far into the future -- with almost no added computation time. A key insight is that human intent can be injected at any location within the transformer sequence if the user decides that the model-predicted actions are inappropriate. At every time step, the user can (1) do nothing and allow autonomous operation to continue while observing the robot's future plan sequence, or (2) take over and momentarily prescribe a different set of actions to nudge the model back on track. We host the videos and other supplementary material at https://sites.google.com/view/assistive-teleop., Comment: 9 pages, 4 figures, 1 table. NeurIPS 2021 Workshop on Robot Learning: Self-Supervised and Lifelong Learning, Virtual, Virtual

The quantification of liver fat as a diagnostic assessment of steatosis remains an important priority for noninvasive imaging systems. We derive a framework in which the unknown fat volume percentage can be estimated from a pair of ultrasound measurements. The precise estimation of ultrasound speed of sound and attenuation within the liver are shown to be sufficient for estimating fat volume assuming a classical model of the properties of a composite elastic material. In this model, steatosis is represented as a random dispersion of spherical fat vacuoles with acoustic properties similar to those of edible oils. Using values of speed of sound and attenuation from the literature where normal and steatotic livers were studied near 3.5 MHz, we demonstrate agreement of the new estimation method with independent measures of fat. This framework holds the potential for translation to clinical scanners where the two ultrasound measurements can be made and utilized for improved quantitative assessment of steatosis., Comment: 28 pages, 5 figures, 2 tables

The speckle statistics of optical coherence tomography images of biological tissue have been studied using several historical probability density functions. A recent hypothesis implies that underlying power-law distributions in the medium structure, such as the fractal branching vasculature, will contribute to power-law probability distributions of speckle statistics. Specifically, these are the Burr type XII distribution for speckle amplitude, the Lomax distribution for intensity, and the generalized logistic distribution for log amplitude. In this study, these three distributions are fitted to histogram data from nine optical coherence tomography scans of various biological tissues and samples. The distributions are also compared with conventional distributions such as the Rayleigh, K, and gamma distributions. The results indicate that these newer distributions based on power laws are, in general, more appropriate models and support the plausibility of their use for characterizing biological tissue. Potentially, the governing power-law parameter of these distributions could be used as a biomarker for tissue disease or pathology.

We derive closed-form solutions for reverberant elastography in anisotropic elastic media by adapting the framework used in electromagnetic theory to treat transverse isotropic materials. Different sample-setup geometries are analyzed, highlighting their relevance for both optical coherence elastography (OCE) and ultrasound elastography (USE). Numerical simulations using finite elements are used to validate the proposed solutions in practical cases. OCE experiments are conducted in ex vivo chicken muscle samples for the characterization of in-plane and out-of-plane shear modulus assuming a transverse isotropic elastic model. Additionally, we obtained a generalized geometry-independent solution for the isotropic media case, thus unifying previous results for reverberant elastography., Comment: 12 pages, 14 figures

Elastography provides significant information on staging of fibrosis in patients with liver disease and may be of some value in assessing steatosis. However, there remain questions as to the role of steatosis and fibrosis as cofactors influencing the viscoelastic measurements of the liver tissues, particularly shear wave speed (SWS) and shear wave attenuation (SWA). In this study, by employing the theory of composite elastic media as well as two independent experimental measurements on fat-in-gelatin phantoms and also finite element simulations, it is consistently shown that fat and fibrosis jointly influence the SWS and SWA measurements. At a constant level of fat, fibrosis stages can influence the SWA by factors of 2-4. Moreover, the rate of increase in SWA with increasing fat is strongly influenced by the stages of fibrosis; softer background cases (low fibrosis stages) have higher rate of SWA increase with fat than those with stiffer moduli (higher fibrosis stages). Meanwhile, SWS results are influenced by the presence of fat, however the degree of variability is more subtle. The results indicate the importance of jointly considering fat and fibrosis as contributors to SWS and SWA measurements in complex liver tissues and in the design and interpretation of clinical trials., Comment: 26 pages, 9 figures

After 100 years of theoretical treatment of speckle patterns from coherent illumination, there remain some open questions about the nature of ultrasound speckle from soft vascularized tissues. A recent hypothesis is that the fractal branching vasculature is responsible for the dominant echo pattern from organs such as the liver. In that case an analysis of cylindrical scattering structures arranged across a power law distribution of sizes is warranted. Using a simple model of echo strength and basic transformation rules from probability, we derive the first order statistics of speckle considering the amplitude, the intensity, and the natural log of amplitude. The results are given by long tailed distributions that have been studied in the statistics literature for other fields. Examples are given from simulations and animal studies, and the theoretical fit to these preliminary data support the overall framework as a plausible model for characterizing ultrasound speckle statistics., Comment: 26 pages, 8 figures

The H-scan approach is a matched filter methodology that aims to add information to the traditional ultrasound B-scan. The theory is based on the differences in the echoes produced by different classes of reflectors or scatterers. Matched filters can be created for different types of scatterers, whereby the maximum output indicates a match and color schemes can be used to indicate the class of scatterer responsible for echoes, providing a visual interpretation of the results. However, within the theory of weak scattering from a variety of shapes, small changes in the size of the inhomogeneous objects will create shifts in the scattering transfer function. In this paper, we determine the shift in center frequency, along with time and frequency domain characteristics of echoes and argue for a general power law transfer function to capture the major characteristics of scattering types. With this general approach, the H-scan matched filters can be set to elicit more fine grain shifts in scattering types, commensurate with more subtle changes in tissue morphology. Compensation for frequency dependent attenuation is helpful for avoiding beam softening effects with increasing depths. Examples from phantoms and normal and pathological tissues are provided to demonstrate that the H-scan analysis and displays are sensitive to scatterer size and morphology, and can be adapted to conventional imaging systems., Comment: 35 pages, 17 figures

Recent theories examine the role of the fractal branching vasculature as a primary site of Born scattering from soft normal tissues. These derivations postulate that the first order statistics of speckle from tissue such as the liver, thyroid, and prostate will follow a Burr distribution with a power law parameter that can be related back to the underlying power law which governs the branching network. However, the issue of scatterer spacing, or the number of cylindrical vessels per sample volume of the interrogating pulse, has not been directly addressed. This is now examined with a 3D simulation that varies the number density and the governing power law parameter of an ensemble of different sized cylinders. The Burr distribution is found to be an appropriate model for the histogram of amplitudes from speckle regions, and the parameters track the underlying conditions. These results are also tested in a more general model of rat liver scans in normal vs. abnormal conditions, and the resulting Burr distributions are also found to be appropriate and sensitive to underlying scatterer distributions. These preliminary results suggest that the classical Burr distribution may be useful in the quantification of scattering of ultrasound from soft vascularized tissues., Comment: 23 pages, 10 figures

A rising wave of technologies and instruments are enabling more labs and clinics to make a variety of measurements related to tissue viscoelastic properties. These instruments include elastography imaging scanners, rheological shear viscometers, and a variety of calibrated stress-strain analyzers. From these many sources of disparate data, a common step in analyzing results is to fit the measurements of tissue response to some viscoelastic model. In the best scenario, this places the measurements within a theoretical framework and enables meaningful comparisons of the parameters against other types of tissues. However, there is a large set of established rheological models, even within the class of linear, causal, viscoelastic solid models, so which of these should be chosen? Is it simply a matter of best fit to a minimum mean squared error of the model to several data points? We argue that the long history of biomechanics, including the concept of the extended relaxation spectrum, along with data collected from viscoelastic soft tissues over an extended range of times and frequencies, and the theoretical framework of multiple relaxation models which model the multi-scale nature of physical tissues, all lead to the conclusion that fractional derivative models represent the most succinct and meaningful models of soft tissue viscoelastic behavior. These arguments are presented with the goal of clarifying some distinctions between, and consequences of, some of the most commonly used models, and with the longer term goal of reaching a consensus among different sub-fields in acoustics, biomechanics, and elastography that have common interests in comparing tissue measurements., Comment: 39 pages, 11 figures

The issue of speckle statistics from ultrasound images of soft tissues such as the liver has a long and rich history. A number of theoretical distributions, some related to random scatterers or fades in optics and radar, have been formulated for pulse-echo interference patterns. This work proposes an alternative framework in which the dominant echoes are presumed to result from Born scattering from fluid filled vessels that permeate the tissue parenchyma. These are modeled as a branching, fractal, self-similar, multi scale collection of cylindrical scatterers governed by a power law distribution relating the number of branches at each radius. A deterministic accounting of the echo envelopes across the scales from small to large is undertaken, leading to a closed form theoretical formula for the histogram of the envelope of the echoes. The normalized histogram is found to be related to the classical Burr distribution, with the key power law parameter directly related to that of the number density of vessels vs. diameter, frequently reported in the range of 2 to 4. Examples are given from liver scans to demonstrate the applicability of the theory., Comment: 26 pages, 14 figures. This article has been submitted to The Journal of the Acoustical Society of America. After it is published, it will be found at http://asa.scitation.org/journal/jas